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The complaint alleges violations of American securities law and was filed on Friday as a class action in federal court in San Francisco.

Mr Musk set off a firestorm with the 53-character post on Tuesday. “Am considering taking Tesla private at $420. Funding Secured," he wrote.

The stock initially shot up 11 percent to almost $380. Then it fell back, losing about 7 percent over two days, as doubts mounted about the feasibility of the going-private idea, and about the chief executive's declaration that funding was already in place.

“Musk’s statement that he had secured funding was especially material and significantly moved the market,” shareholder Kalman Isaacs said in the complaint.

“Because Musk has not secured financing, and has issued false and materially misleading information into the market, short sellers of Tesla stock were forced to cover their positions by purchasing shares at artificially inflated prices after 12:48pm on August 7, 2018. Obviously, all purchasers of Tesla securities were injured as well.”

The shares climbed again late on Thursday following a report that the board planned to meet with financial advisers to formalise a process for going private and would ask Mr Musk to recuse himself from these discussions. His personal stake in Tesla is almost 20 percent.

The US Securities and Exchange Commission is examining whether Mr Musk’s tweet was meant to be factual, intensifying its scrutiny of Tesla’s public statements after the announcement, according to people familiar with the matter.